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Transcript
Chapter 19 DC Circuits Units of Chapter 19 • EMF and Terminal Voltage • Resistors in Series and in Parallel • Kirchhoff’s Rules • EMFs in Series and in Parallel; Charging a Battery • Circuits Containing Capacitors in Series and in Parallel Units of Chapter 19 • RC Circuits – Resistor and Capacitor in Series • Electric Hazards • Ammeters and Voltmeters Objectives: The students will be able to: •Distinguish between the emf and the terminal voltage of a battery and calculate the terminal voltage given the emf, internal resistance of the battery, and external resistance in the circuit. •Determine the equivalent resistance of resistors arranged in series or in parallel or the equivalent resistance of a series parallel combination. Resistors in circuits To determine the current or voltage in a circuit that contains multiple resistors, the total resistance must first be calculated. Explain that resistors can be combined in series or parallel. 19.1 EMF and Terminal Voltage Electric circuit needs battery or generator to produce current – these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf: (19-1) 19.1 EMF and Terminal Voltage This resistance behaves as though it were in series with the emf. EMF vs. Terminal Voltage • For current to flow through a circuit, we need a device to supply the electrical energy, ie: a battery • A device that supplies electrical energy to a circuit is called the source of what is referred to as the Electromotive Force or EMF ( ) • EMF is a misnomer because the battery does not deliver a force in Newtons • The potential difference ΔV=Vab , is measured across the terminals of a battery • When no current is drawn from the battery, Vab = which is determined from the chemical reactions in the battery Internal Resistance • The battery is not a constant source of current because of internal losses within the battery • The chemical reaction that produces the electrical energy also produces heat, and may be modeled as a resistor internal to the battery. This is called the internal resistance “r”. Battery Circuit Vab V I r where I Rr • The terminal voltage is always smaller than the EMF Practice problem – p.521 Circuits • Can either be series or parallel. Series Circuit • Three lamps connected in a daisy-chain fashion can be considered as three resistors in series Series • Current only takes one path for electrons • Current flows through every part of the circuit Lights in a Series Series • If you add a resistor (like another light): –Total resistance goes UP since all the current has must go through each resistor. Adding Resistors to Series: –Current in the circuit will go DOWN (lights will dim) –If you remove a light bulb or one burns out—all go out! Current in Series • Current is the same at all points • Use Ohm’s Law to find current using resistance and voltage 19.2 Resistors in Series and in Parallel A series connection has a single path from the battery, through each circuit element in turn, then back to the battery. 19.2 Resistors in Series and in Parallel The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage. (19-2) 19.2 Resistors in Series and in Parallel From this we get the equivalent resistance (that single resistance that gives the same current in the circuit). (19-3) Resistors in Series When connected in series, the total resistance (Rt) is equal to: Rt = R1 + R2 + R3 +… The total resistance is always larger than any individual resistance because all of the current must go through each resistor. Sample Problem Calculate the total current through the circuit. 15 Ω 10 Ω 6 Ω Rt = 15 Ω +10 Ω + 6 Ω Rt = 31 Ω I = V/Rt = 10 V/ 31 Ω = 0.32 A 10 V Resistors in Series Since charge has only one path to flow through, the current that passes through each resistor is the same. The sum of all potential differences equals the potential difference across the battery. > R value = > V Value 5V 3V 2V 10 V Resistance in series circuits Use Ohm’s law to calculate the voltage across the resistors in the next slide. Write your values in the voltmeters and see if they agree with the actual readings. .603 Amps 2.2 Ω 1.5 Ω .897 1.332 Volts Volts What should the voltage across the two resistors be? .601 Amps 2.2 Ω 1.5 Ω 2.231 Volts Equivalent resistance The two resistors in the previous series circuit can be thought of as a single resistor. Work out and write the equivalent resistance using Ohm’s law and the values of current and voltage shown. 2.231 V 3.7 Ω 0.601 A Equivalent resistance In a series circuit the total resistance of the components is the sum of the resistance of each component. So, the equivalent resistance R is found as: R = R1 + R2 R1 R2 R 2.2 Ω 1.5 Ω 3.7 Ω 19.2 Resistors in Series and in Parallel A parallel connection splits the current; the voltage across each resistor is the same: Parallel Circuits Has at least one point where current divides More than one path for current to flow Paths are also known as branches Lights in Parallel Parallel: If you add a resistor: Total resistance goes down Total current goes up when you add another path Removing a Light Bulb If you remove a light bulb or one burns out, the others stay on because the circuit is still closed. Current in Parallel Current flows into a branching point, the same total current must flow out again Current depends on resistance in each branch Voltage in Parallel Voltage is the same across each branch – because each branch is on the same wire Resistance in Parallel Calculate current in each branch based on resistance in each branch by using Ohm’s Law Parallel Circuit • Three lamps connected across each other can be modeled as three resistors in parallel R1R2 • For only 2 resistors in parallel, Req becomes: Req R1 R2 19.2 Resistors in Series and in Parallel The total current is the sum of the currents across each resistor: 19.2 Resistors in Series and in Parallel This gives the reciprocal of the equivalent resistance: (19-4) Resistors in Parallel When connected in parallel, the total resistance (Rt) is equal to: 1/Rt = 1/R1 + 1/R2 + 1/R3 +… Due to this reciprocal relationship, the total resistance is always smaller than any individual resistance. Sample Problem Calculate the total resistance through this segment of a circuit. 1/Rt = 1/12 Ω +1/4 Ω + 1/6 Ω 12 Ω 4Ω = 1/12 Ω + 3/12 Ω + 2/12 Ω 1/Rt = 6/12 Ω = ½ Ω Rt = 2 Ω 6Ω Resistors in Parallel Since there is more than one possible path, the current divides itself according to the resistance of each path. smallest resistor = more current passes largest resistor = least current passes Resistors in Parallel The voltage across each resistor in a parallel combination is the same. 10 V 10 V 10 V 10 V Calculate the total resistance in the circuit below 3Ω 2Ω 6Ω 4Ω Rtot = 3 Ω + 2 Ω = 5 Ω Rtot = 6 Ω + 4 Ω = 10 Ω Rtot = 3 1/3 Ω + - 1/Rtot = 2/10 Ω+ 1/10 Ω = 3/10 Ω Resistance in parallel circuits Look at the parallel circuit on the next slide and work out the current in the main circuit and through each resistor in the parallel branches. What do you think the current in the main circuit should be? 1.830 1.991 Volts Amps 2.2 Ω 0.832 A 1.716 Volts 1.144 A 1.5 Ω Resistance in parallel circuits The current in the main circuit is the sum of the currents in the parallel branches: I I1 R1 I2 R2 I = I 1 + I2 19.2 Resistors in Series and in Parallel An analogy using water may be helpful in visualizing parallel circuits: Gravitational potential difference is the same for both pipes, just as voltage is the same for parallel resistors. If both pipes are open, twice as much water will flow through. With two equal pipes open, the net resistance to the flow of water will be reduced, by half, just as for electrical circuits in parallel. If both pipes are closed, the dam offers infinite resistance to the flow of water. This corresponds in the electrical case to an open circuit, no current- infinite resistance. Toll Road—Circuit Analogy Toll Booth Explanation Adding toll booths in series increases resistance and slows the current flow. Adding toll booths in parallel lowers resistance and increases the current flow. Batteries in Series and Parallel: In series—The voltage is increased. In parallel—No change in voltage; these batteries will last longer! Homework Questions chapter 19 #1, 4, 7 Problems #1, 5, 7, 9, 15, 17 Elaboration Physics Classroom activities phET activities